Resonators form a key component of a timing or frequency reference. The resonators are actuated to oscillate near the natural resonant frequency. This natural resonant frequency depends on the material and shape of the resonators.
For reference applications, it is desired that the resonant frequency is precisely controlled. For typical applications, the required frequency accuracy ranges from 1 to 100 part per million (ppm). This ppm level accuracy requires extremely good manufacturing tolerances. In addition, final calibration in the form of mechanical and/or electrical adjustment is often performed.
Micromechanical resonators have been widely used as a key component in MEMS devices, such as micro-gyroscopes, microvibromotors, micro-engines and microwave systems. The resonators are actuated, e.g. electrostatically, to oscillate near the natural resonant frequency.
Furthermore, micromechanical resonators are may also be used to complement quartz technology in frequency references. However, the frequency accuracy of micromechanical resonators needs to be improved before they can challenging the quartz technology.
Micromechanical resonators that are made by a combination of optical lithography and etching processes offer size and cost advantages over conventional quartz crystal resonators. However, the manufacturing variations in a micromechanical process can be several percentages of the devices dimensions.
For a better understanding of the prior art relation to the present invention reference will be made to the accompanying drawings, in which:
FIG. 1 illustrates a basic mechanical resonator according to prior art.
FIG. 2 illustrates a lumped model for the basic mechanical resonator according to prior art.
FIG. 1 illustrates a basic mechanical resonator according to prior art. A simple resonator consists of a spring element 1 and a rectangular mass 2. The spring element 1 can for example be a mechanical cantilever spring 1 as shown in FIG. 1.
In a simple resonator of FIG. 1, the resonant frequency ω0 is given by
                                          ω            0                    =                                    k              m                                      ,                            (        1        )            where the spring constant k is given by
                    k        =                  Y          ⁢                                          ⁢                                                                      w                  3                                ⁢                h                                            4                ⁢                                  L                  3                                                      .                                              (        2        )            
FIG. 2 illustrates a lumped model for the basic mechanical resonator according to prior art. Here Y is the Young's modulus for the material, w is the width of the spring element, h is the height of the spring element, and L is the spring element length. The spring element width w is typically small and due to cubic dependency, the resonant frequency ω0 is very sensitive to the variations in spring element width w.
The first-order change of the resonant frequency ω0 with respect to spring element width w is
                                                        Δω              0                                      ω              0                                =                                    3              2                        ⁢                                          Δ                ⁢                                                                  ⁢                w                            w                                      ,                            (        3        )            where ∂ω0 is the infinitesimal frequency change due to the infinitesimal spring element width change ∂w. One of the most significant problems in the design of micromechanical resonators is the variation of the resonant frequency, which is caused by poor dimensional precision in the structures. In resonators manufactured using the means of micromechanics, there may be quite substantial dimensional tolerance errors.
For example, following from the above equation (Equation 3), if the spring element width varies by 4%, the resonant frequency varies by 6% or 60,000 ppm. To reduce this variation, it is desired that the resonant frequency is relatively unaffected by the manufacturing variations.
Thus, the object of the invention is to provide a structure of a micromechanical resonator which has an improved frequency accuracy in comparison to the prior art solutions. The present invention meets this need.